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Linear Interpolation Calculator

Estimate a value between two known data points.

About Linear Interpolation Calculator

Linear interpolation assumes the relationship is straight between the two points, which is usually reasonable over a short span. The calculator flags when the target falls outside the known range. Interpolation is safe; extrapolation assumes the pattern continues, which is exactly the assumption that most often fails.

Formula

Linear Interpolation

y = y₁ + (x − x₁)(y₂ − y₁) ÷ (x₂ − x₁)

interpolation
Estimating inside the known range, generally reliable
extrapolation
Estimating outside it, considerably less reliable

Worked example

With the default values below, Linear Interpolation Calculator returns Interpolated Value of 124.000000. Change any input above and every figure here is recalculated in your browser.

Inputs used

First x value
10
First y value
100
Second x value
20
Second y value
160
Target x value
14

Results

Interpolated Value
124.000000
Slope Between the Points
6.000000
Position Between the Points
40.000%
Interpolation or Extrapolation
Interpolation — the target lies between the known points
Y-Intercept of the Line
40.00000

Step by step

  1. 1Values used
  2. 2Linear Interpolation
  3. 3Interpolated Value= 124.000000
  4. 4Slope Between the Points= 6.000000
  5. 5Position Between the Points= 40.000
  6. 6Interpolation or Extrapolation= Interpolation — the target lies between the known points
  7. 7Y-Intercept of the Line= 40.00000

Assumptions and limits

  • The result is derived only from the 5 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 6 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

How is Linear Interpolation calculated?

y = y₁ + (x − x₁)(y₂ − y₁) ÷ (x₂ − x₁) Linear interpolation assumes the relationship is straight between the two points, which is usually reasonable over a short span. The calculator flags when the target falls outside the known range.

Why does Linear Interpolation matter?

Interpolation is safe; extrapolation assumes the pattern continues, which is exactly the assumption that most often fails.

What values do I need to enter?

This calculator takes 5 inputs: First x value, First y value, Second x value, Second y value, Target x value. The pre-filled defaults are a realistic starting point — replace them with figures from your own environment for a result you can act on.

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